This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
An important goal of seismic prospecting is to accurately image subsurface structures commonly referred to as reflectors. Seismic prospecting is facilitated by obtaining raw seismic data during performance of a seismic survey. During a seismic survey, seismic energy can be generated at ground or sea level by, for example, a controlled explosion (or other form of source, such as vibrators), and delivered to the earth. Seismic waves are reflected from underground structures and are received by a number of sensors/receivers, such as geophones. The seismic data received by the geophones is processed in an effort to create an accurate mapping of the underground environment. The processed data is then examined with a goal of identifying geological formations that may contain hydrocarbons (e.g., oil and/or natural gas).
Full Wavefield Inversion (FWI) is a seismic method capable of utilizing the full seismic record, including the seismic events that are treated as “noise” by standard inversion algorithms. The goal of FWI is to build a realistic subsurface model by minimizing the misfit between the recorded seismic data and synthetic (or modeled) data obtained via numerical simulation.
It has been well accepted that, for reflection dominant data, conventional FWI (e.g., Tarantola, 1984) lacks the ability to update long wavelengths of the velocity model and requires an accurate starting model to converge to a geologically meaningful result. If such conventional FWI starts with a relatively “poor” starting model, where the kinematic differences between the simulated data and the observed data are greater than half of the dominant wavelength, it often gets stuck in local minima because of cycle skipping (when the travel time difference between events simulated numerically in the computer and those acquired in the field exceeds half the period corresponding to the dominant frequency of the data).
Several FWI algorithms proposed for reflection FWI are based on scale separation between high and long wavenumber components of the velocity model (Xu 2012, Tang 2013, Tang U.S. patent application Ser. No. 13/849,270). These methods hinge on the following premise: FWI's difficulty of updating the low-wavenumber components of the model is due to the weakness of the tomographic terms in the gradient of the FWI. It is also observed that the gradient of a conventional FWI algorithm contains strong high and mid wavenumber information, but very weak low wavenumber information. For this reason, it is believed that FWI predominantly updates the short wavelength components. The proposed remedy in the above-noted documents is to enhance one term of the gradient versus the other, and recombine them to form a new gradient to improve FWI on reflection-dominant data.
The success of Xu and Tang approaches noted above is limited by the adequacy of the starting velocity model. When the starting velocity model contains strong long wavelength anomalies, the corresponding reflectors are located far from their true position, and as a result of this conventional FWI can't recover long wavelength anomalies (AlTheyab, 2015). There are several approaches for overcoming this problem. One is to use global optimization techniques, but their success is limited to very special cases due to computational complexity of the global optimization algorithms. Another approach is to use the so-called extended space methods (Symes, 2008), where the inversion space is extended in some parameter space (such as shot, offset etc.). In addition, these methods also add an extra term to the objective function as a control of coherency (flatness, focusing etc.). Although the reported results are promising, the extended space method approach is prohibitively expensive due to the computational cost. To make FWI algorithms practical for field data application, it is desirable to use local optimization methods and keep the original formulation. The present technological advancement provides a technical solution to above-noted problem of not being able to recover strong long wavelength anomalies.